Mixed Buchsbaum--Rim Multiplicities

Mathematics – Commutative Algebra

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

AmS-TeX-Ver 2.1 with amsppt.sty-ver 2.1c. The introduction was made more readable, and a number of minor correction were made.

Scientific paper

We prove the results about mixed Buchsbaum--Rim multiplicities announced in (9.10)(ii) on p.224 of our recent paper [J.Alg.(1994)], including a general mixed-multiplicity formula. In addition, we identify these multiplicities as the coefficients of the ``leading form'' of the appropriate Buchsbaum-Rim polynomial in three variables, and we prove a positivity theorem. In fact, we define the multiplicities as the degrees of certain zero-dimensional ``mixed twisted'' Segre classes, and we develop an encompassing general theory of these new rational equivalence classes in all dimensions. In parallel, we develop a theory of pure ``twisted'' Segre classes, and we recover the main results in [J.Alg.(1994)] about the pure Buchsbaum--Rim multiplicities, the polar multiplicities, and so forth. Moreover, we identify the additivity theorem [J.Alg.(1994), (6.7b)(i), p.205] as giving a sort of residual-intersection formula, and we show its (somewhat unexpected) connection to the mixed-multiplicity formula. Also, we work in a more general setup than before, and we develop a new approach, based on the completed normal cone.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Mixed Buchsbaum--Rim Multiplicities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mixed Buchsbaum--Rim Multiplicities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mixed Buchsbaum--Rim Multiplicities will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-93071

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.